Some invariant subalgebras are graded isolated singularities

TL;DR

This paper proves that certain invariant subalgebras of skew polynomial algebras under permutation actions are graded isolated singularities, confirming a conjecture by Chan-Young-Zhang.

Contribution

It establishes that the invariant subalgebra of the (-1)-skew polynomial algebra under permutation is a graded isolated singularity, validating a prior conjecture.

Findings

Invariant subalgebra is a graded isolated singularity

Confirms the conjecture of Chan-Young-Zhang

Advances understanding of skew polynomial algebra invariants

Abstract

In this note, we prove that the invariant subalgebra of the (-1)-skew polynomial algebra under a permutation action is a graded isolated singularity, and thus a conjecture of Chan-Young-Zhang is true.